Quantum computing utilizes quantum particles to carry out computational processes. The fundamental unit of quantum information is called a quantum bit or qubit. A qubit can be both a zero and a one at the same time. An example is the spin of an electron, wherein the up or down spin can correspond to a zero, a one, or a superposition of states in which it is both up and down at the same time. Performing a calculation using the electron essentially performs the operation simultaneously for both a zero and a one. Experimental advances in quantum computation have come most rapidly in nuclear magnetic resonance (NMR) and ion-trap systems. The success of few-qubit quantum computation in such systems demonstrates an urgent need for a quantum computing scheme that is scaleable to a large number of qubits. Solid-state qubits are one of the primary candidates. Numerous proposals have been made for solid-state quantum computers. These proposals include the use of nuclear spins as qubits, B. E. Kane, “A Silicon-Based Nuclear Spin Quantum Computer,” Nature, Vol. 393 (6681), (1998), pp. 133–137; and the use of electronic spins as quantum dots, DiVincenzo, et al., “Quantum Computers and Quantum Coherence,” J. of Magnetism and Magnetic Materials, Vol. 200, (1–3), 1999, pp. 202–218. Potential issues with such proposed systems include individual impurity spins, as well as gate operation and readout methods for the quantum dots.
Spins can be manipulated using a strong DC magnetic field combined with a spatially uniform radio frequency field (e.g., at GHz frequencies). In the presence of a small g-factor gradient, the spins can be addressed individually. Entanglement of one spin with another proceeds by gating the barrier between spins. This gives rise to a time-dependent exchange interaction, H(t)=J(t)S1S2. A combination of these operations acting in the proper sequence on two qubits will produce a controlled-NOT gate (C-NOT). See, e.g., R. Vrijen, et al., “Electron-Spin Resonance Transistors for Quantum Computing and Silicon-Germanium Heterostructures,” Physical Review A, Atomic, Molecular, and Optical Physics, Vol. 62(1), 2000, pp. 012306/1–10.
Quantum computation also can be performed without g-factor tuning and the individual spin rotations via high frequency radiation that g-factor tuning allows. Instead, the time-dependent exchange interaction, H(t)=J(t)S1S2, can be used in combination with coded qubits, as described in D. P. DiVencenzo, D. Bacon, J. Kempe, G. Burkard, K. B. Whaley, Nature (London) 408, 339 (2002), in which a single qubit is represented by the total wave function of several individual spins. In this way, the exchange interaction alone enables universal quantum computation.
Several approaches have been proposed for the implementation of spin qubits in semiconductors. See, D. Loss, et al., Phys. Rev. A57, 120, (1998); B. E. Kane, Nature (London) 393, 133, (1998); R. Vrijen, et al., Phys. Rev. A62, 012306 (2000); J. Levy, Phys. Rev. A64, 052306 (2001); M. Friesen, et al., Phys. Rev. B 67, 121301-1–4 (2003). Several components of qubit technology have been demonstrated, as discussed in J. M. Elzerman, et al., Phys. Rev. B 67, 161308(R) (2003). However, the combined challenge of preparing, storing and measuring spins is formidable. The measurement of spin qubits is a particular challenge. On the one hand, qubits should be well isolated from their environment to avoid decoherence, and on the other hand, it is necessary to individually couple the qubits to an external measurement device. Qubit initialization involves an additional dissipative coupling to the environment. For quantum computing, it is necessary to initiate such coupling selectively, and with sufficient strength to perform the operations quickly. Indeed, scalable quantum computing relies on fault-tolerant quantum error correction algorithms, involving frequent, parallel measurements, and a steady supply of initialized qubits. P. W. Shor, Proceedings of the 35th Annual Symposium on Foundations of Computer Science, S. Goldwasser, Ed., IEEE Computer Society Press, Los Alamitos, Calif., 1994, pp. 124 et seq.; A. M. Steane, Phys. Rev. A 68, 042322 (2003). Rapid and sensitive quantum measurement techniques involving radio frequency single electron transistors (rf-SETs) have been developed. K. W. Lehnert, et al., Phys. Rev. Lett. 90, 027002 (2003). Rf-SETs have been used to detect the tunneling of individual electrons in semiconductor devices, as discussed in L. Lu, et al., Nature (London) 423, 422 (2003).
Quantum dot architectures have been developed specifically for the purpose of manipulating electron spins for fast and accurate two-qubit operations that serve as universal gates for quantum computations. M. Friesen, et al., (2003) supra. See, also, U.S. Pat. No. 6,597,010. Recent experimental results have shown that decoherence does not pose a fundamental problem for such gate operations. A. M. Tyryshkin, et al., Phys. Rev. B 68, 193207 (2003). Using special qubit geometries as discussed in M. Friesen, et al., Appl. Phys. Lett. 81, 4619 (2002), it should be possible to perform reliable gate operations in silicon quantum dots at rates between about 1 MHz and 1 GHz. It would be desirable to be able to achieve similar speeds and reliable operation for measurement and initialization operations. One technique for converting spin information to charge information is discussed in D. Loss, et al., supra, and the use of single electron transistors to read out the resulting spin state has been proposed by Kane, et al., (1998) supra, who posit spin-dependent charge motion onto impurities in silicon. In I. Martin, et al., Phys. Rev. Lett. 90, 018301 (2003), a scheme is proposed for single spin readout that also converts spin information into charge information in an electron trap near a conducting channel. Resistance of the channel depends on the occupation of the trap, which in turn can be made to depend on the spin.